Abstract
We consider multiverses as time-amalgamated multiply warped products of Lorentzian (Einstein) manifolds. We define the Local Multiverse as a time-connected component associated with our physical (3 + 1)-spacetime. It is a collection of “parallel universes” with (mutually) synchronized timelines. Metaphysical considerations suggest that the Local Multiverse could be an extremely complex agglomeration with, at least, several hundred parallel universes in the Solar neighbourhood (and many thousands in galaxy bulks). In this paper we study a simplified time-almagamated globally hyperbolic model. Our picture implies the multiversality of elementary particles which are, actually, transcosmic (super)strings with multiple endpoints on parallel universes considered as D-branes.
Highlights
By definition, a spacetime or universe ( X, g ) in this paper means a connected time-oriented (n +1) -dimensional Lorentzian manifold of signature (1, n)
Metaphysical considerations suggest that the Local Multiverse could be an extremely complex agglomeration with, at least, several hundred parallel universes in the Solar neighbourhood
In this paper we study a simplified time-almagamated globally hyperbolic model
Summary
A spacetime or universe ( X , g ) in this paper means a connected time-oriented (n +1) -dimensional Lorentzian manifold of signature (1, n). The product of two universes with dimensions m +1 and n +1 gives a pseudo-Riemmanian manifold of signature (2, m + n). When timelines of two universes are synchronized, we can take time-amalgamated products and coproducts. It leads to the natural definition of multiverses as such amalgamated (co)products. There is a unique timeline (up to appropriate synchronizations) in all parallel universes of the same multiverse.
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